For a detailed treatment on quantum information we refer the reader to [1]}. A register in this paper can contain a classical or a quantum state. The classical state of a register \(\mathsf {X}\)  is described by a finite alphabet \(\Sigma \) . An example alphabet used in this paper is \(\Sigma = \mathbb {F}_2^n\) . The quantum state of \(\mathsf {X}\)  is described by the set of density operators \(\mathrm {D}(\mathcal {X})\)  where \(\mathcal {X}\)  is the complex Euclidean space \(\mathbb {C}^\Sigma \) .
